

A065775


Array T read by diagonals: T(i,j)=least number of knight's moves on a chessboard (infinite in all directions) needed to move from (0,0) to (i,j).


17



0, 3, 3, 2, 2, 2, 3, 1, 1, 3, 2, 2, 4, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 2, 2, 2, 4, 4, 5, 3, 3, 3, 3, 3, 3, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 3, 3, 3, 3, 5, 5, 5, 6, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 6, 6, 6, 6, 4, 4, 4, 4, 4, 6, 6, 6, 6, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7
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OFFSET

0,2


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LINKS



FORMULA

T(i,j) is given in cases:
Case 1: row 0
T(0,0)=0, T(1,0)=3, and for m>=1,
T(4m2,0)=2m, T(4m1,0)=2m+1, T(4m,0)=2m,
T(4m+1,0)=2m+1.
Case 2: row 1
T(0,1)=3, T(1,1)=2, and for m>=2,
T(4m2,1)=2m1, T(4m1,1)=2m, T(4m,1)=2m+1,
T(4m+1,1)=2m+2.
Case 3: columns 1 and 2
(column 1) = (row 1); (column 2 = row 2).
Case 4: For i>=2 and j>=2,
T(i,j)=1+min{T(i2,j1),T(i1,j2)}.
Cases 14 determine T in the 1st quadrant;
all other T(i,j) are easily obtained by symmetry.


EXAMPLE

T(i,j) for 2<=i<=2 and 2<=j<=2:
4 1 2 1 4=T(2,2)
1 2 3 2 1=T(2,1)
2 3 0 3 2=T(2,0)
1 2 3 2 1=T(2,1)
4 1 2 1 4=T(2,2)
Corner of the array, T(i,j) for i>=0, k>=0:
0 3 2 3 2 3 4...
3 2 1 2 3 4 3...
2 1 4 3 2 3 4...
3 2 3 2 3 4 2...


CROSSREFS

Identical to A049604 except for T(1, 1).


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EXTENSIONS



STATUS

approved



